Least Squares Algorithms for Constructing Constrained Ultrametric and Additive Tree Representations of Symmetric Proximity Data

Journal of Classification, Volume 4, Issue 2, pp 155-173, 1987

19 Pages Posted: 10 Jul 2017

See all articles by Geert De Soete

Geert De Soete

Ghent University

J. Carroll

Rutgers, The State University of New Jersey (Deceased)

Wayne S. DeSarbo

Pennsylvania State University

Date Written: September 1987

Abstract

A mathematical programming algorithm is developed for fitting ultrametric or additive trees to proximity data where external constraints are imposed on the topology of the tree. The two procedures minimize a least squares loss function. The method is illustrated on both synthetic and real data. A constrained ultrametric tree analysis was performed on similarities between 32 subjects based on preferences for ten odors, while a constrained additive tree analysis was carried out on some proximity data between kinship terms. Finally, some extensions of the methodology to other tree fitting procedures are mentioned.

Keywords: Hierarchical clustering, Path length trees, Mathematical programming, Constrained classification methods

Suggested Citation

De Soete, Geert and Carroll, J. and DeSarbo, Wayne S., Least Squares Algorithms for Constructing Constrained Ultrametric and Additive Tree Representations of Symmetric Proximity Data (September 1987). Journal of Classification, Volume 4, Issue 2, pp 155-173, 1987, Available at SSRN: https://ssrn.com/abstract=2784845

Geert De Soete

Ghent University ( email )

Coupure Links 653
Gent, 9000
Belgium

J. Carroll

Rutgers, The State University of New Jersey (Deceased)

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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